If the position vector of a point P is \(2\hat{\imath}-\hat{\jmath}+3\hat{k}\) and \(\overrightarrow{PQ}=\hat{\imath}+4\hat{\jmath}-2\hat{k}\), then the position vector of the point Q is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(3\hat{\imath}+3\hat{\jmath}+\hat{k}\)
Let O be the origin. By the triangle law of addition,
\(\overrightarrow{OQ} = \overrightarrow{OP}+\overrightarrow{PQ}\)
Adding the components:
\(\overrightarrow{OQ} = (2+1)\hat{\imath}+(-1+4)\hat{\jmath}+(3-2)\hat{k}\)
\( = 3\hat{\imath}+3\hat{\jmath}+\hat{k}\)